Any arguments for the decorated function are just passed to __call__(). The output is:

Inside __init__()
After decoration
Preparing to call sayHello()
Inside __call__()
sayHello arguments: say hello argument list
After self.f(*args)
After first sayHello() call
Inside __call__()
sayHello arguments: a different set of arguments
After self.f(*args)
After second sayHello() call

Notice that __init__() is the only method called to perform decoration, and __call__() is called every time you call the decorated sayHello().

Now the process of decoration calls the constructor and then immediately invokes __call__(), which can only take a single argument (the function object) and must return the decorated function object that replaces the original. Notice that __call__() is now only invoked once, during decoration, and after that the decorated function that you return from __call__() is used for the actual calls.

Although this behavior makes sense -- the constructor is now used to capture the decorator arguments, but the object __call__() can no longer be used as the decorated function call, so you must instead use __call__() to perform the decoration -- it is nonetheless surprising the first time you see it because it's acting so much differently than the no-argument case, and you must code the decorator very differently from the no-argument case.

The return value of the decorator function must be a function used to wrap the function to be decorated. That is, Python will take the returned function and call it at decoration time, passing the function to be decorated. That's why we have three levels of functions; the inner one is the actual replacement function.

Because of closures, wrapped_f() has access to the decorator arguments arg1, arg2 and arg3, without having to explicitly store them as in the class version. However, this is a case where I find "explicit is better than implicit," so even though the function version is more succinct I find the class version easier to understand and thus to modify and maintain.